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Algebra Discrete Math., 2013, Volume 16, Issue 1, Pages 20–32 (Mi adm431)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

On locally nilpotent derivations of Fermat rings

P. Brumattia, M. Velosob

a IMECC-Unicamp, Rua Sérgio Buarque de Holanda 651, Cx. P. 6065, 13083-859, Campinas-SP, Brazil
b Defim-UFSJ, Rodovia MG 443 Km 7, 36420-000, Ouro Branco-MG, Brazil

Abstract: Let $B_n^m =\frac{\mathbb{C}[X_1,\ldots, X_n]}{(X_1^m+\cdots +X_n^m)}$ (Fermat ring), where $m\geq2$ and $n\geq3$. In a recent paper D. Fiston and S. Maubach show that for $m\geq n^2-2n$ the unique locally nilpotent derivation of $B_n^m$ is the zero derivation. In this note we prove that the ring $B_n^2$ has non-zero irreducible locally nilpotent derivations, which are explicitly presented, and that its ML-invariant is $\mathbb{C}$.

Keywords: Locally Nilpotente Derivations, ML-invariant, Fermat ring.

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Bibliographic databases:
MSC: 14R10, 13N15, 13A50
Received: 06.09.2010
Revised: 05.04.2013
Language:

Citation: P. Brumatti, M. Veloso, “On locally nilpotent derivations of Fermat rings”, Algebra Discrete Math., 16:1 (2013), 20–32

Citation in format AMSBIB
\Bibitem{BruVel13}
\by P.~Brumatti, M.~Veloso
\paper On locally nilpotent derivations of Fermat rings
\jour Algebra Discrete Math.
\yr 2013
\vol 16
\issue 1
\pages 20--32
\mathnet{http://mi.mathnet.ru/adm431}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184695}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Veloso, I. Shestakov, “Rings of constants of linear derivations on Fermat rings”, Commun. Algebr., 46:12 (2018), 5469–5479  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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